In traditional diffusion MRI, short pulsed field gradients (PFG) are used for the diffusion encoding. The standard Stejskal-Tanner sequence uses one single pair of such gradients, known as single-PFG (sPFG). In this work we describe how trajectories in q-space can be used for diffusion encoding. We discuss how such encoding enables the extension of the well-known scalar b-value to a tensor-valued entity we call the diffusion measurement tensor. The new measurements contain information about higher order diffusion propagator covariances not present in sPFG. As an example analysis, we use this new information to estimate a Gaussian distribution over diffusion tensors in each voxel, described by its mean (a diffusion tensor) and its covariance (a 4th order tensor).

In this paper we construct an atlas that summarizes functional connectivity characteristics of a cognitive process from a population of individuals. The atlas encodes functional connectivity structure in a low-dimensional embedding space that is derived from a diffusion process on a graph that represents correlations of fMRI time courses. The functional atlas is decoupled from the anatomical space, and thus can represent functional networks with variable spatial distribution in a population. In practice the atlas is represented by a common prior distribution for the embedded fMRI signals of all subjects. We derive an algorithm for fitting this generative model to the observed data in a population. Our results in a language fMRI study demonstrate that the method identifies coherent and functionally equivalent regions across subjects. The method also successfully maps functional networks from a healthy population used as a training set to individuals whose language networks are affected by tumors.

Current neuroimaging investigation of the white matter typically focuses on measurements derived from diffusion tensor imaging, such as fractional anisotropy (FA). In contrast, imaging studies of the gray matter oftentimes focus on morphological features such as cortical thickness, folding and surface curvature. As a result, it is not clear how to combine findings from these two types of approaches in order to obtain a consistent picture of morphological changes in both gray and white matter. In this paper, we propose a joint investigation of gray and white matter morphology by combining geometrical information from white and the gray matter. To achieve this, we first introduce a novel method for computing multi-scale white matter tract geometry. Its formulation is based on the differential geometry of curve sets and is easily incorporated into a continuous scale-space framework. We then incorporate this method into a novel framework for "fusing" white and gray matter geometrical information. Given a set of fiber tracts originating in a particular cortical region, the key idea is to compute two scalar fields that represent geometrical characteristics of the white matter and of the surface of the cortical region. A quantitative marker is created by combining the distributions of these scalar values using Mutual Information. This marker can be then used in the study of normal and pathological brain structure and development. We apply this framework to a study on autism spectrum disorder in children. Our preliminary results support the view that autism may be characterized by early brain overgrowth, followed by reduced or arrested growth (Courchesne, 2004).

For accurate estimation of the ensemble average diffusion propagator (EAP), traditional multi-shell diffusion imaging (MSDI) approaches require acquisition of diffusion signals for a range of b-values. However, this makes the acquisition time too long for several types of patients, making it difficult to use in a clinical setting. In this work, we propose a new method for the reconstruction of diffusion signals in the entire q-space from highly undersampled sets of MSDI data, thus reducing the scan time significantly. In particular, to sparsely represent the diffusion signal over multiple q-shells, we propose a novel extension to the framework of spherical ridgelets by accurately modeling the monotonically decreasing radial component of the diffusion signal. Further, we enforce the reconstructed signal to have smooth spatial regularity in the brain, by minimizing the total variation (TV) norm. We combine these requirements into a novel cost function and derive an optimal solution using the Alternating Directions Method of Multipliers (ADMM) algorithm. We use a physical phantom data set with known fiber crossing angle of 45° to determine the optimal number of measurements (gradient directions and b-values) needed for accurate signal recovery. We compare our technique with a state-of-the-art sparse reconstruction method (i.e., the SHORE method of Cheng et al. (2010)) in terms of angular error in estimating the crossing angle, incorrect number of peaks detected, normalized mean squared error in signal recovery as well as error in estimating the return-to-origin probability (RTOP). Finally, we also demonstrate the behavior of the proposed technique on human in vivo data sets. Based on these experiments, we conclude that using the proposed algorithm, at least 60 measurements (spread over three b-value shells) are needed for proper recovery of MSDI data in the entire q-space.

Multivoxel pattern analysis (MVPA) is a sensitive and increasingly popular method for examining differences between neural activation patterns that cannot be detected using classical mass-univariate analysis. Recently, Todd et al. ("Confounds in multivariate pattern analysis: Theory and rule representation case study", 2013, NeuroImage 77: 157-165) highlighted a potential problem for these methods: high sensitivity to confounds at the level of individual participants due to the use of directionless summary statistics. Unlike traditional mass-univariate analyses where confounding activation differences in opposite directions tend to approximately average out at group level, group level MVPA results may be driven by any activation differences that can be discriminated in individual participants. In Todd et al.’s empirical data, factoring out differences in reaction time (RT) reduced a classifier’s ability to distinguish patterns of activation pertaining to two task rules. This raises two significant questions for the field: to what extent have previous multivoxel discriminations in the literature been driven by RT differences, and by what methods should future studies take RT and other confounds into account? We build on the work of Todd et al. and compare two different approaches to remove the effect of RT in MVPA. We show that in our empirical data, in contrast to that of Todd et al., the effect of RT on rule decoding is negligible, and results were not affected by the specific details of RT modelling. We discuss the meaning of and sensitivity for confounds in traditional and multivoxel approaches to fMRI analysis. We observe that the increased sensitivity of MVPA comes at a price of reduced specificity, meaning that these methods in particular call for careful consideration of what differs between our conditions of interest. We conclude that the additional complexity of the experimental design, analysis and interpretation needed for MVPA is still not a reason to favour a less sensitive approach.

Deformable image registration is used increasingly in image-guided interventions and other applications. However, validation and characterization of registration performance remain areas that require further study. We propose an analysis methodology for deriving tolerance limits on the initial conditions for deformable registration that reliably lead to a successful registration. This approach results in a concise summary of the probability of registration failure, while accounting for the variability in the test data. The (β, γ) tolerance limit can be interpreted as a value of the input parameter that leads to successful registration outcome in at least 100β% of cases with the 100γ% confidence. The utility of the methodology is illustrated by summarizing the performance of a deformable registration algorithm evaluated in three different experimental setups of increasing complexity. Our examples are based on clinical data collected during MRI-guided prostate biopsy registered using publicly available deformable registration tool. The results indicate that the proposed methodology can be used to generate concise graphical summaries of the experiments, as well as a probabilistic estimate of the registration outcome for a future sample. Its use may facilitate improved objective assessment, comparison and retrospective stress-testing of deformable.

Guiding diffusion tract-based anatomy by functional magnetic resonance imaging (fMRI), we aim to investigate the relationship between structural connectivity and functional activity in the human brain. To this purpose, we introduced a novel groupwise fMRI-guided tractographic approach, that was applied on a population ranging between prodromic and moderate stages of Alzheimer’s disease (AD). The study comprised of 15 subjects affected by amnestic mild cognitive impairment (aMCI), 14 diagnosed with AD and 14 elderly healthy adults who were used as controls. By creating representative (ensemble) functionally guided tracts within each group of participants, our methodology highlighted the white matter fiber connections involved in verbal fluency functions for a specific population, and hypothesized on brain compensation mechanisms that potentially counteract or reduce cognitive impairment symptoms in prodromic AD. Our hope is that this fMRI-guided tractographic approach could have potential impact in various clinical studies, while investigating white/gray matter connectivity, in both health and disease.

Many studies have observed altered neurofunctional and structural organization in the aging brain. These observations from functional neuroimaging studies show a shift in brain activity from the posterior to the anterior regions with aging (PASA model), as well as a decrease in cortical thickness, which is more pronounced in the frontal lobe followed by the parietal, occipital, and temporal lobes (retrogenesis model). However, very little work has been done using diffusion MRI (dMRI) with respect to examining the structural tissue alterations underlying these neurofunctional changes in the gray matter. Thus, for the first time, we propose to examine gray matter changes using diffusion MRI in the context of aging. In this work, we propose a novel dMRI based measure of gray matter "heterogeneity" that elucidates these functional and structural models (PASA and retrogenesis) of aging from the viewpoint of diffusion MRI. In a cohort of 85 subjects (all males, ages 15-55 years), we show very high correlation between age and "heterogeneity" (a measure of structural layout of tissue in a region-of-interest) in specific brain regions. We examine gray matter alterations by grouping brain regions into anatomical lobes as well as functional zones. Our findings from dMRI data connects the functional and structural domains and confirms the "retrogenesis" hypothesis of gray matter alterations while lending support to the neurofunctional PASA model of aging in addition to showing the preservation of paralimbic areas during healthy aging.

The normal human brain is characterized by a pattern of gross anatomical asymmetry. This pattern, known as the "torque", is associated with a sexual dimorphism: The male brain tends to be more asymmetric than that of the female. This fact, along with well-known sex differences in brain development (faster in females) and onset of psychosis (earlier with worse outcome in males), has led to the theory that schizophrenia is a disorder in which sex-dependent abnormalities in the development of brain torque, the correlate of the capacity for language, cause alterations in interhemispheric connectivity, which are causally related to psychosis (Crow TJ, Paez P, Chance SE. 2007. Callosal misconnectivity and the sex difference in psychosis. Int Rev Psychiatry. 19(4):449-457.). To provide evidence toward this theory, we analyze the geometry of interhemispheric white matter connections in adolescent-onset schizophrenia, with a particular focus on sex, using a recently introduced framework for white matter geometry computation in diffusion tensor imaging data (Savadjiev P, Kindlmann GL, Bouix S, Shenton ME, Westin CF. 2010. Local white geometry from diffusion tensor gradients. Neuroimage. 49(4):3175-3186.). Our results reveal a pattern of sex-dependent white matter geometry abnormalities that conform to the predictions of Crow’s torque theory and correlate with the severity of patients’ symptoms. To the best of our knowledge, this is the first study to associate geometrical differences in white matter connectivity with torque in schizophrenia.